function bezier_curve(t, p0, p1, p2, p3, p4) = 
    pow(1-t, 4) * p0 + 
    4 * pow(1-t, 3) * t * p1 + 
    6 * pow(1-t, 2) * pow(t, 2) * p2 +
    4 * (1-t) * pow(t, 3) * p3 +
    pow(t, 4) * p4;

function curved_polygon(points, steps, x_shift, y_shift) = 
    let(
        left_curve = [for (t = [0 : 1/steps : 1])
            bezier_curve(t, points[0], points[1], points[2], points[3], points[4])
        ],
        right_curve = [for (pt = left_curve)
            [pt[0] + x_shift, pt[1] + y_shift]
        ]
    )
    concat(left_curve, [for (i = [len(right_curve)-1 : -1 : 0]) right_curve[i]]);

module base() {
    rotate_extrude() {
        polygon(curved_polygon(
            points = [
                [-80, 30],
                [-50, 15],
                [-50, 0],
                [-50, -15],
                [-80, -30]
            ],
            steps = 100,
            x_shift = 50,
            y_shift = 0
        ));
    }
}

base();